论文标题
Confluent Virasoro Fusion内核和非多项式$ Q $ -ASKEY计划的家族
The family of confluent Virasoro fusion kernels and a non-polynomial $q$-Askey scheme
论文作者
论文摘要
我们研究了最近引入的Confluent Virasoro Fusion内核家族$ \ MATHCAL {C} _K（b，\boldsymbolθ，σ_s，ν）$。我们研究了他们的本本函数属性，并表明它们可以被视为连续双$ q $ -hahn和大$ Q $ -JACOBI多项式的非多功能概括。更准确地说，我们证明：（i）$ \ MATHCAL {C} _K $是四个不同的差异操作员的共同特征功能$ \ MATHCAL {C} _k $ degnerates to $ q $ -jacobi多项式当$σ_s$被适当离散时。这些观察结果使我们提出了$ Q $ -ASKEY计划的非多功能概括的存在。这种非单位方案的最高成员是Virasoro Fusion内核（或等效地，Ruijsenaars的超几何函数），其第一个汇合由$ \ Mathcal {C} _K $给出。
We study the recently introduced family of confluent Virasoro fusion kernels $\mathcal{C}_k(b,\boldsymbolθ,σ_s,ν)$. We study their eigenfunction properties and show that they can be viewed as non-polynomial generalizations of both the continuous dual $q$-Hahn and the big $q$-Jacobi polynomials. More precisely, we prove that: (i) $\mathcal{C}_k$ is a joint eigenfunction of four different difference operators for any positive integer $k$, (ii) $\mathcal{C}_k$ degenerates to the continuous dual $q$-Hahn polynomials when $ν$ is suitably discretized, and (iii) $\mathcal{C}_k$ degenerates to the big $q$-Jacobi polynomials when $σ_s$ is suitably discretized. These observations lead us to propose the existence of a non-polynomial generalization of the $q$-Askey scheme. The top member of this non-polynomial scheme is the Virasoro fusion kernel (or, equivalently, Ruijsenaars' hypergeometric function), and its first confluence is given by the $\mathcal{C}_k$.
